A nonsmooth Levenberg-Marquardt method for vertical complementarity problems
type: Item
instance of: scholarly article
title: A nonsmooth Levenberg-Marquardt method for vertical complementarity problems
zbMATH Open document ID: 1421.65015
author: Linsen Song
author: Yan Gao
published in: Numerical Algorithms
publication date: 2017-11-17T00:00:00Z
review text: In this paper, the vertical complementarity problem is studied. The problem is reformulated as a system of nonsmooth equations \(H(x)=0\). For solving this system, the nonsmooth Levenberg-Marquardt (LM) method with double parameter adjusting strategy is presented. The method is based on the computation of an element in the B-differential of a mapping \(H\) which along with a suitable choice of the LM parameter are the critical issues in the LM method. The LM parameter is adjusted based on the norm of the vector-valued minimum function and the ratio between the current and the predicted reductions. The authors investigate the computation of at least one element in the B-differential of \(H\) as it is necessary in the implementation of the algorithm, show the global convergence, and discuss the local convergence rate of the algorithm under the local error bound condition.
reviewed by: Ctirad Matonoha
Mathematics Subject Classification ID: 65K10
Mathematics Subject Classification ID: 90C33
Mathematics Subject Classification ID: 49M15
Mathematics Subject Classification ID: 49J52
zbMATH DE Number: 6808526
zbMATH Keywords: vertical complementarity problem
zbMATH Keywords: nonsmooth equations
zbMATH Keywords: nonsmooth analysis
zbMATH Keywords: Levenberg-Marquardt method
zbMATH Keywords: B-differential
zbMATH Keywords: global convergence
zbMATH Keywords: local convergence
zbMATH Keywords: local error bound condition
zbMATH Keywords: algorithms
MaRDI profile type: Publication
full work available at URL: s11075-017-0267-3
OpenAlex ID: W2581959465
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DOI: 10.1007/S11075-017-0267-3
description: scientific article; zbMATH DE number 6808526